A railway truck on a level, straight track is initially at rest. The truck is given a quick, horizontal push by an engine so that it now rolls along the track.

push from engine
railway truck
v = 4.3 m s–1
The engine is in contact with the truck for a time T = 0.54 s and the initial speed of the truckafterthepushis4.3ms–1. Themassofthetruckis2.2×103kg.
Due to the push, a force of magnitude F is exerted by the engine on the truck. The sketch shows how F varies with contact time t.

(i) Determine the magnitude of the maximum force Fmax exerted by the engine on
the truck. [4]
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pls help

consider the tuck

F*time=impulse=mass*change invelocity
Force=masstruck*4.3/.54 N
Now that is the average force.
It goes from max, to zero. So Fmax=2*Favg
= 2*masstruck*4.3/.54

To determine the magnitude of the maximum force Fmax exerted by the engine on the truck, we can use the concept of impulse-momentum.

Impulse is defined as the change in momentum of an object, and it can be calculated using the formula:

Impulse = Force × Time

Since the force is constant in this scenario, we can rewrite the formula as:

Impulse = F × Δt

Where Δt is the change in time during which the force is applied. In this case, the change in time is equal to the contact time T, which is given as 0.54 s.

Impulse = F × T

The impulse experienced by the truck can also be expressed as the change in momentum, which is the mass of the truck multiplied by the change in velocity:

Impulse = mass × change in velocity

Impulse = 2.2 × 10^3 kg × 4.3 m/s

Since the initial velocity is zero, the change in velocity is simply the final velocity:

Impulse = 2.2 × 10^3 kg × 4.3 m/s

Now we can equate the impulse from the force and from the change in momentum:

F × T = 2.2 × 10^3 kg × 4.3 m/s

We can rearrange this equation to solve for the maximum force Fmax:

Fmax = (2.2 × 10^3 kg × 4.3 m/s) / 0.54 s

Calculating this gives us the magnitude of the maximum force exerted by the engine on the truck.

To determine the magnitude of the maximum force Fmax exerted by the engine on the truck, you can use the impulse-momentum principle. Impulse is defined as the change in momentum of an object, and it is equal to the product of force and time.

The equation for impulse is given by:

Impulse = Force x Time

Since the initial momentum of the truck is zero (as it was initially at rest), the impulse exerted by the engine on the truck is equal to the final momentum of the truck.

The equation for momentum is given by:

Momentum = Mass x Velocity

The final momentum of the truck can be calculated as:

Final Momentum = Mass x Final Velocity

Plugging in the given values, we can calculate the final momentum:

Final Momentum = (2.2 x 10^3 kg) x (4.3 m/s)

After calculating the final momentum, you can substitute it back into the impulse equation to solve for the force:

Impulse = Force x Time

(2.2 x 10^3 kg) x (4.3 m/s) = Force x 0.54 s

Now you can solve for the force:

Force = (2.2 x 10^3 kg x 4.3 m/s) / 0.54 s

Simplifying the equation:

Force = 17,356 N

Therefore, the magnitude of the maximum force Fmax exerted by the engine on the truck is 17,356 Newtons.