1)A particle of mass0.70kg moves along thex-axis with a potential energy whose dependence onxis shown below.(a)What is the force on the particle (in N) at

x= 2.0,

5.0, 8.0, and12 m?(Indicate the direction with the signs of your answers.)x = 2.0 mF= Nx= 5.0 mF= Nx= 8.0 mF= Nx= 12 mF= N(b)If the total mechanical energyEof the particle is

8.0J,

what are the minimum and maximum positions of the particle (in m)?minimum mmaximum m(c)What are these positions (in m) if

E=6.0J?

minimum mmaximum m(d)If

E=19J,

what are the speeds of the particle (in m/s) at the positions listed in part (a)?x = 2.0 mv= m/sx= 5.0 mv= m/sx= 8.0 mv= m/sx= 12 mv= m/s

2)A particle with a mass

m = 8.00 kg

is moving along the x axis under the influence of the potential energy function

U(x) = (2.00 J/m²)x² 32.0 J.

If the particle is released from rest at the position

x = 6.40 m,

determine the following. (The sign is important. Be sure not to round intermediate calculations.)(a) total mechanical energy of the particle at any position J (b) potential energy of the particle at the position

x = 3.80 m

J (c) kinetic energy of the particle at the position

x = 3.80 m

J (d) maximum speed of the particle as it travels along the x axis m/s (e) acceleration of the particle at the position

x = 3.80 m

(Indicate the direction with the sign of your answer.) m/s² (f) maximum position the particle may obtain along the x axis m

3)A particle with a mass

m = 8.00 kg

is moving along the x axis under the influence of the potential energy function

U(x) = (2.00 J/m²)x² 32.0 J.

If the particle is released from rest at the position

x = 6.40 m,

determine the following. (The sign is important. Be sure not to round intermediate calculations.)(a) total mechanical energy of the particle at any position J (b) potential energy of the particle at the position

x = 3.80 m

J (c) kinetic energy of the particle at the position

x = 3.80 m

J (d) maximum speed of the particle as it travels along the x axis m/s (e) acceleration of the particle at the position

x = 3.80 m

(Indicate the direction with the sign of your answer.) m/s² (f) maximum position the particle may obtain along the x axis m

4)A block of mass200g is attached to a spring of spring constant88N/m(see the following figure). The other end of the spring is attached to a support while the mass rests on a rough surface with a coefficient of friction of0.18that is inclined at angle of30.The block is pushed along the surface till the spring compresses by15cmand is then released from rest.(a)How much potential energy (in J) was stored in the block-spring-support system when the block was just released? J(b)Determine the speed of the block (in m/s) when it crosses the point where the spring is neither compressed nor stretched. m/s(c)Determine the position of the block where it just comes to rest on its way up the incline. (Enter the distance in centimeters along the incline past the point where the spring is neither compressed nor stretched.) cm