Question

A fan exerts a force of 10 N on a frictionless cart of mass 250 g, accelerating the cart from rest over a distance of 0.5 m. The same fan is then used to accelerate a 500 g cart from rest over the same distance. Select ALL statements below that are TRUE about this situation:

A) The energy transferred to both carts is different.

B) The work done by the fan in both cases is the same.

C) The final kinetic energy of both carts is the same.

D) The final velocity of both carts is different.

Answer 1

Given:

A fan exerts a force of 10 N

F = 10 N

there are two carts

mass of first cart = m1 = 250 g

and mass of second cart = m2 = 500 g

both the carts are accelerated from rest and over a same distance of 0.5 m

s = 0.5 m

Now,

CASE 1:

mass = m1 = 250 g

s= 0.5 m

F = 10 N

work done by the force/fan = force * displacement = F*s = (10 N) * (0.5 m) = 5 Nm

energy transferred = workd one by fan = 5 Nm

cart is at rest so change in kinetic energy = final kinrtic energy = work done by fan = 5 Nm

So,

CASE 1:

mass = m2 = 500 g

s= 0.5 m

F = 10 N

work done by the force/fan = force * displacement = F*s = (10 N) * (0.5 m) = 5 Nm

energy transferred = workd one by fan = 5 Nm

cart is at rest so change in kinetic energy = final kinrtic energy = work done by fan = 5 Nm

So,

Now, on comparing both the cases above let us discuss the options.

A) FALSE (Energy is same 5 Nm)

B) TRUE (work done by fan in both is same (5 Nm), as force and displacement is same for both)

C) TRUE (same for both 5 Nm)

D) TRUE (final velocity is different (v_1 and v_2) )

In case of any doubt please discuss in comment section below.