A cart with mass m rolls along a track to the right with a speed vo. It strikes a bumper and rebounds with speed of vo/2. a) Use the impulse-momentum to write an equation for the system which is the cart only. b) If the time during which the bumper exerts a force on the cart is t, write an expression for the force F exerted on the cart in terms of the given variables.

a. I =  -3mv₀/2 b. F = -3mv₀/2t

Explanation:

a. Use the impulse-momentum to write an equation for the  system which is the cart only.

We know Impulse , I = Δp where Δp = change in momentum.

Now, Δp = m(v - u) where m = mass of cart, u = initial velocity of cart = v₀ and v = rebound velocity of cart = -v₀/2 (negative since it moves in the opposite direction to u)

So, I =  Δp = m(v - u)

Substituting the values of the variables into the equation, we have

I = m(-v₀/2 - v₀) = -3mv₀/2

So, I =  -3mv₀/2

b. If the time during which the bumper exerts a force on the cart is t, write an expression for the force F exerted on the cart in terms of the given variables.

We know impulse I = Ft where F = force exerted on the cart and t = time force acts

Also, I = -3mv₀/2

So, Ft = -3mv₀/2

F = -3mv₀/2t