Question

The graphs below show the force applied to a 250 g cart and the resulting motion.

Forie v 1o is 2o 2s 3035

a)How much work was done on the car?

b)How much thermal energy was produced (i.e. how much energy was dissipated by friction)

Answer 1

"Mass of the cart is m = 250g = 0.250kg (a) we know that work done = force times displacement that is ""Area under the force vs. displacement graph will provide the work done."" w = w_1 + w_2 w = 1/2 times 4 times (10 times 10^- 2 m) + 4 times (20 times 10^- 2 m) w = 0.2 + 0.8 w = 1 Joul \r\n (b) initial velocity of the cart is v_i = 0 m/s final velocity of the cart is v_f = 2 m/s Now from energy conservation work done = change in kinetic energy + that loss w = 1/2 mv^2_f - 1/2 mv^2_i + Heat loss 1 = 1/2 times 0.250 times (2)^2 - 0 + Heat loss 1 = 0.5 + Heat loss Heat loss = 0.5 Joul This is the energy dissipated by the friction."