A glider of mass 1500 kg is launched from rest on a straight and level track using a catapult.

Question 15

A glider of mass 1500 kg is launched from rest on a straight and level track using a catapult. The graph shows the variation with time of the resultant force.

What is the speed of the glider when the resultant force acting on it reaches zero?

A 133 m s^-1                       B 200 m s^-1                       C 250 m s^-1                       D 267 m s^-1

Reference: Past Exam Paper – November 2015 Paper 11 Q11

Solution:

Answer: A.

From Newton’s second law:

F = Δp / t

F × t = Δp

(F × t) is the impulse.

 

The change in momentum is given by the impulse, i.e. average force × time or the area under the graph.

Area under graph = Δp = F × t = ½ × 40 × 10 = 200 kNs

Δp = 200 000 Ns

Δp = m(Δv)

Dividing by the mass then gives the change in speed.

Initially, the glider is at rest. i.e. initial speed = 0

Δp = m(v–0) = mv       where v is the final speed

mv = 200 000 Ns

Speed v = 200 000 / 1500 = 133 m s^-1