Please show you work so that I could understand it better and then preform everything on my own.

c) What IS the force exerted by the block on the inclined plane Ht that scenario? 301 A curve has a radius of R and a banking angle of I), Assuming a static coefcient of friction [1' of the car's tires to the road, what is the speed you can safely use for the car to not slide up or down the embankment? A Draw a FBD of the car on the banks B Solve for the required speed. C What would happen if the car's speed was lower than your answer from (B)? I) What would happen if the car's speed was higher than your answer from (B)? E Assuming there is absolutely no friction between the car's tires and the road - could the car still get around the curve? If so, what is the precise speed required? If not, explain. Hint: How can you change your answer from (B) to model this new sitr uation? 31 A 500 g particle is released from rest at point A on the inside of a sm0& Please calculate the following: 31 A 500 3 particle is released from rest at point A on the inside of a smooth hemispherical bowl of radius R=50 cm. Please calculate the following: A) lts gravitational energy at A relative to that at B. B) Kinetic energy at 8. C) Speed at B. D) Potential energy at C relative to that at B. E) Speed at C. 31A block of mass 2 kg is sent siiding onto a frictionless surface at a velocity of 5 m/s. It collides with a stationary block of mass 1 kg. After the collision the 2 kg block is deflected at an angle of 45 degrees with the incoming direction. It the final velocity of the 2 kg block is 2 m/s, find the following: A] initial momentum of the combined system of the two blocks in X and V directions. B) Final momentum of the 2 kg block in X and Y directions. C) Final momentum of the 1 kg block in X and Y directions. D) Angle that the 1 kg block makes with the incoming direction after collision. E) Speed of the 1 kg block after collision. b) d) 33. A uniform rod of length L and mass M is allowed to rotate freely about a frictionless pin mounted as shown in the figure, It Is released from rest at a horizontal posrtiont What is the Initial potential energy of the system? (Take the configuration where the rod is hanging straight down as the zero potential energy reference), What is the kinetic energy of the system when it reaches the vertical configuration What is the angular velocity of the rod at the vertical configuration? What is the speed of the centre of mass when it passes the lowest paint in its trajectory? 34. Two astronauts with mass 100 kg are connected by a 10 m rope. They are isolated in space and are rotating about their centre of mass at a speed of 1 m/s. 3) What is their combined angular momentum? b) What is the rotational energy of the system? c) If they pull the rope to shorten the distance between them to 5 In, what is the new angular momentum of the system? all What is their new angular velocity? e) What is the work done by the astronauts to shorten the rope? Z / /, Z 35. Weight ofthe uniform rod is w1=100 N. w2=200 N, L=3 m. n) Draw n ll'EB body dingmin ol the rod involving forces wt, WE and forces of support at A and C, ol What are the unknown variables in the problem? cl Generate two equations by halancnig forces on the rod in horizontal and vertical directions. d) Generate one equation iiSing the net torque about A. e) Solve the above three equations to obtain the lorce exerted on the red at the hinge. 36) A sailboat starts from the beach and travels 20 km at an angle of45 degrees south of east. They then turn and travel an additional 10 km at an angle of 30 degrees north of east. (ConSIder the initial paint as the origin of the coordinate system, the beach along the xiaxis and east pointing along the positive x7 axis.) e) Solve the above three equations to obtain the force exerted on the rod at the hinge. 36) A sailboat starts from the beach and travels 20 km at an angle of 45 degrees south of east. They then turn and travel an additional 10 km at an angle of 30 degrees north of east. (Consider the initial point as the origin of the coordinate system, the beach along the x-axis and east pointing along the positive it- axts.) (at Draw a diagram ofthe router (b) How far does the boat travel in the x direction during the first stage? (c) How far does the boat travel in the y direction during the second stage of the trip? (d) Express the final displacement of the boat in terms of Its x and y components. (e) Determine the final displacement of the boat from the beach in both magnitude and direction. 37) A football player shootha m with an angle of 45 degrees from the around. Assume the Dlaver aims straight at the anal and an initial velocitv of 37) A football player shoots the ball onto the goal from a distance of 25 m with an angle of 45 degrees from the ground. Assume the player aims straight at the goal and an initial velocity of V=ZO m/s. ignore any air registance. (a) Draw a sketch of the trajectory Including the ball and the goal. (b) Find the equations describing the x and y component of the ball. (c) How long does the ball travel until it reaches the goal? (Hint: Use the x coordinate) (d) Calculate the y component when the ball reaches the goal. Does the player score a goal? A typical goal has a height of 2.44 m. (e) If the ball had an initial velocity of 15 n1/s, would the player score a goal? 38) A hotair balloon rises straight up With a velouty of v: 5 m/s relative to earth. Assume a person travelling in a train observes the situation, The train travels with a velocity of v: 30 m/s relative to earth towards east. 3) Draw a schematic of the situation from the perspective of an observer at rest and one schematic from the perspective of the traveller in the train. In both schematics indicate the approximate direction of travel of both the balloon and the train. b) What are the velocity vectors of the balloon and the train relative to earth? cl What is the velocity vector of the balloon relative to the train? d) What is the apparent angle of the balloon from the perspective of the person on the train? Hint: Draw the velocity vector of the balloon in a coordinate system. 39) A child sits on a sled with a total mass of 100 kg (sled + child) which rests on an inclined frictionless plane with an angle of 30 degrees. 3) Draw a free body diagram (leave space for part d). b) Calculate the downhill force pointing parallel to the plane. 6) Assuming the slope iwl the child reaches I'kn luxnnm nitkn kill) sc ema IC rorn e perspec ive o e rave er In e rain. n 0 5c erna Ics in- approximate direction of travel of both the balloon and the train. b) What are the velocity vectors of the balloon and the train relative to earth? cl What is the velomty vector of the balloon relative to the train? d) What Is the apparent angle of the balloon from the perspective of the person on the train? Hint: Draw the velocny vector of the balloon in a coordinate system, 39) A child sits on a sled with a total mass of 100 kg (sled + child) which rests on an inclined frictionless plane with an angle of 30 degrees. 3) Draw a free body diagram (leave space for part (1). b) Calculate the downhill force pointing parallel to the plane. c) Assuming the slope is 50 m long, how long does it take until the child reaches the bottom ofthe hill? d) Now, we start pulling the sled and the child up the hill again. We pull at an angle of 60 degrees from the plane. Include the applied force in your free body diagram from a). How much force do we need to apply such that the sled does not move? not move? 40) A car is driving on a banked curve. The curve has a radius of R = 300m and the banking angle is 9 = 20 degrees. Assume a constant banking and a constant coefficient of friction p=0.8. a) Draw a free~body diagram of the car of the banked curve. b) Solve for the maximal velocity of the car such that it does not slide up the curve. c) What happens if the car's speed is lower than your answer from b? d) Suppose it rained in the morning and there are still wet patches on the curve, reducing the friction coefficient to #:02. What happens if the car is still going at the same speed as initially? e) Assuming there is no friction between the car and the road, could the car still get around the curve? If yes, what is the velocity? If no, explain. Hint: Use your formula from b. 41) Two weights of mass m1: 10kg and m2=5kg are connected by a weightless string paWe lighter block is at rest on the eround. The heavier block is released from rest at a