Questions and Answers of Engineering Mechanics Dynamics

The graph shows the rectilinear acceleration of a particle as a function of time over a 12-second interval. If the particle is at rest at the position s0 = 0 at time t = 0, determine the velocity of
The cart impacts the safety barrier with speed v0 = 3.25 m/s and is brought to a stop by the nest of nonlinear springs which provide a deceleration a = −k1x − k2x3, where x is the amount of
Reconsider the rollout of the space-shuttle orbiter of the previous problem. The drag chute is deployed at 200 mi/hr, the wheel brakes are applied at 100 mi/hr until wheel stop, and the drag chute is
The 230,000-lb space-shuttle orbiter touches down at about 220 mi/hr. At 200 mi/hr its drag parachute deploys. At 35 mi/hr, the chute is jettisoned from the orbiter. If the deceleration in feet per
A particle moves along the x-axis with the velocity history shown. If the particle is at the position x = −4 in. at time t = 0, plot the corresponding displacement history for the time interval 0
If the velocity v of a particle moving along a straight line decreases linearly with its displacement s from 20 m/s to a value approaching zero at s = 30 m, determine the acceleration a of the
A vacuum-propelled capsule for a high-speed tube transportation system of the future is being designed for operation between two stations A and B, which are 10 km apart. If the acceleration and
An electric car is subjected to acceleration tests along a straight and level test track. The resulting v-t data are closely modeled over the first 10 seconds by the function v = 24 t − t2 + 5√t,
A model rocket is launched from rest with a constant upward acceleration of 3 m/s2 under the action of a small thruster. The thruster shuts off after 8 seconds, and the rocket continues upward until
A particle moving along a straight line has an acceleration which varies according to position as shown. If the velocity of the particle at the position x = −5 ft is v = −2 ft/sec, determine the
Car A is traveling at a constant speed vA = 130 km/h at a location where the speed limit is 100 km / h. The police officer in car P observes this speed via radar. At the moment when A passes P, the
Small steel balls fall from rest through the opening at A at the steady rate of two per second. Find the vertical separation h of two consecutive balls when the lower one has dropped 3 meters.
A train which is traveling at 80 mi/hr applies its brakes as it reaches point A and slows down with a constant deceleration. Its decreased velocity is observed to be 60 mi/hr as it passes a point 1/2
A Scotch-yoke mechanism is used to convert rotary motion into reciprocating motion. As the disk rotates at the constant angular rate ω, a pin A slides in a vertical slot causing the slotted member
The main elevator A of the CN Tower in Toronto rises about 350 m and for most of its run has a constant speed of 22 km/h. Assume that both the acceleration and deceleration have a constant magnitude
At a football tryout, a player runs a 40-yard dash in 4.25 seconds. If he reaches his maximum speed at the 16-yard mark with a constant acceleration and then maintains that speed for the remainder of
During an 8-second interval, the velocity of a particle moving in a straight line varies with time as shown. Within reasonable limits of accuracy, determine the amount Δa by which the acceleration
The pilot of a jet transport brings the engines to full takeoff power before releasing the brakes as the aircraft is standing on the runway. The jet thrust remains constant, and the aircraft has a
A car comes to a complete stop from an initial speed of 50 mi/hr in a distance of 100 ft. With the same constant acceleration, what would be the stopping distance s from an initial speed of 70 mi/hr?
A ball is thrown vertically up with a velocity of 30 m/s at the edge of a 60-m cliff. Calculate the height h to which the ball rises and the total time t after release for the ball to reach the
In the pinewood-derby event shown, the car is released from rest at the starting position A and then rolls down the incline and on to the finish line C. If the constant acceleration down the incline
Experimental data for the motion of a particle along a straight line yield measured values of the velocity v for various position coordinates s. A smooth curve is drawn through the points as shown in
Ball 1 is launched with an initial vertical velocity v1 = 160 ft/sec. Three seconds later, ball 2 is launched with an initial vertical velocity v2. Determine v2 if the balls are to collide at an
A particle in an experimental apparatus has a velocity given by v = k√s, where v is in millimeters per second, the position s is millimeters, and the constant k = 0.2 mm1/2s−1. If the particle
Calculate the constant acceleration a in g’s which the catapult of an aircraft carrier must provide to produce a launch velocity of 180 mi/hr in a distance of 300 ft. Assume that the carrier is at
The acceleration of a particle is given by a = c1 + c2v, where a is in millimeters per second squared, the velocity v is in millimeters per second, and c1 and c2 are constants. If the particle
The acceleration of a particle is given by a = −ks2, where a is in meters per second squared, k is a constant, and s is in meters. Determine the velocity of the particle as a function of its
The acceleration of a particle is given by a = −kt2, where a is in meters per second squared and the time t is in seconds. If the initial velocity of the particle at t = 0 is v0 = 12 m/s and the
The acceleration of a particle is given by a = 2t − 10, where a is in meters per second squared and t is in seconds. Determine the velocity and displacement as functions of time. The initial
The displacement of a particle which moves along the s-axis is given by s = (−2 + 3t)e−0.5t, where s is in meters and t is in seconds. Plot the displacement, velocity, and acceleration versus
The velocity of a particle which moves along the s-axis is given by v = 2 − 4t + 5t3/2, where t is in seconds and v is in meters per second. Evaluate the position s, velocity v, and acceleration a
The position of a particle is given by s = 0.27t3 − 0.65t2 − 2.35t + 4.4, where s is in feet and the time t is in seconds. Plot the displacement, velocity, and acceleration as functions of time
The velocity of a particle is given by v = 25t2 − 80t − 200, where v is in feet per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 6 seconds of
The weight of one dozen apples is 5 lb. Determine the average mass of one apple in both SI and U.S. units and the average weight of one apple in SI units. In the present case, how applicable is the
Determine the dimensions of the quantity where ρ is density and v is speed.
Determine the base units of the expression in both SI and U.S. units. The variable m represents mass, g is the acceleration due to gravity, r is distance, and t is time. E mgr dt
Determine the ratio RA of the force exerted by the sun on the moon to that exerted by the earth on the moon for position A of the moon. Repeat for moon position B. Sunlight AO B
Consider a woman standing on the earth with the sun directly overhead. Determine the ratio Res of the force which the earth exerts on the woman to the force which the sun exerts on her. Neglect the
Determine the angle θ at which a particle in Jupiter’s circular orbit experiences equal attractions from the sun and from Jupiter. Use Table D /2 of Appendix D as needed. Sun my + Jupiter Not to
Calculate the distance d from the center of the earth at which a particle experiences equal attractions from the earth and from the moon. The particle is restricted to the line through the centers of
Determine the distance h for which the spacecraft S will experience equal attractions from the earth and from the sun. Use Table D/2 of Appendix D as needed. SX- Sun h Earth 200 000 km Not to scale
A space shuttle is in a circular orbit at an altitude of 200 mi. Calculate the absolute value of g at this altitude and determine the corresponding weight of a shuttle passenger who weighs 180 lb
Determine the absolute weight and the weight relative to the rotating earth of a 60-kg woman if she is standing on the surface of the earth at a latitude of 35°.
At what altitude h above the north pole is the weight of an object reduced to one-third of its earth-surface value? Assume a spherical earth of radius R and express h in terms of R.
Two uniform spheres are positioned as shown. Determine the gravitational force which the titanium sphere exerts on the copper sphere. The value of R is 40 mm. y Сopper 2R 6R 35° R Titanium Problem
Consider two iron spheres, each of diameter 100 mm, which are just touching. At what distance r from the center of the earth will the force of mutual attraction between the contacting spheres be
Determine your mass in slugs. Convert your weight to newtons and calculate the corresponding mass in kilograms.
For the given vectors V1 and V2, determine V1 + V2, V1 + V2, V1 − V2, V1 × V2, V2 × V1, and V1∙V2. Consider the vectors to be non dimensional. y V2 = 12 V = 15 60° x- Problem 1/3
For the 3500-lb car, determine (a) its mass in slugs, (b) its weight in newtons, and (c) its mass in kilograms. W = 3500 lb Problem 1/1

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