Worksheet: Force as Rate of Momentum Change

In this worksheet, we will practice relating the rate of change of momentum of an object to the force acting on it, using the formula ∆p = Ft.

Q1:

An average force of 12.5 N is applied by moving air to a bicycle and its rider, of total mass 80 kg, while it is windy that day. The force is applied throughout a time interval of 0.8 s as the gust of wind is very brief. The wind blows from directly behind the bicycle. What is the total momentum change?

Q2:

A man running on a road had a momentum of 360 kg⋅m/s. The road ahead of the man was covered by sand. The man ran through the sand for 12 seconds and his momentum when he had crossed the sand-covered part of the road was 330 kg⋅m/s. What average force did the sand apply to the man while he ran across it?

Q3:

A force of 10 N is applied to an object for 3 seconds, acting in the direction in which the object is moving. How much does the momentum of the object change?

Q4:

An object increases its momentum by 10 kg⋅m/s in a time of 5 seconds. What average force was applied to the object in that time?

Q5:

A tennis racquet hits a tennis ball that has a mass of 60.5 g and applies a constant 75 N force to it. The tennis ball changes its velocity by 30 m/s during the collision. For how many seconds does the collision last?

Q6:

A frog of mass 30 g jumping into the air from a resting position accelerates to a speed of 12 cm/s in 0.025 s. How many newtons of force did the frog’s legs exert in the jump?

Q7:

A bicycle and its rider have a total mass of 72 kg, and they initially moved at a constant speed of 9 m/s. The bicycle was ridden in a straight line through a puddle for a time of 1.2 s and, when the bicycle had crossed the puddle, it had a momentum of 540 kg⋅m/s. What average force was applied to the bicycle by the puddle?

Q8:

A car has an initial momentum of 1 500 kg⋅m/s when the driver starts to speed it up, changing its momentum to 1 750 kg⋅m/s in a time of 0.75 s. Determine the average force that acts on the car’s wheels while it accelerates. Answer to the nearest newton.

Q9:

An object with an initial momentum of 20 kg⋅m/s is acted on by an average force of 2.5 N and comes to rest. For how long does the force act on the object?

Q10:

An object is decelerated by an average force of 15 N for a time of 0.5 s. What is the change in the object’s momentum?

Q11:

An object that has a momentum of 12 kg⋅m/s is acted on by a constant force for 8 seconds, after which the object’s momentum is 6 kg⋅m/s. Determine the force that acted on the object.

Q12:

A force of 8 N is applied to an object and the object’s momentum increases by 2 kg⋅m/s. How long is the force applied for?

Q13:

Which of the following formulas correctly relates the force acting on an object, the time for which that force acts, and the change in the momentum 𝑝 of the object?

  • A 𝐹 = 1 2 Δ 𝑝 Δ 𝑡
  • B 𝐹 = Δ 𝑡 Δ 𝑝
  • C 𝐹 = 2 Δ 𝑝 Δ 𝑡
  • D 𝐹 = Δ 𝑝 Δ 𝑡
  • E 𝐹 = Δ 𝑝 Δ 𝑡

Q14:

The graph shows how the momentum of an object changes over the time interval 𝑡 = 0 s to 𝑡 = 7 s .

What constant force is applied to the object between 𝑡 = 2 s and 𝑡 = 3 s ?

What constant force is applied to the object between 𝑡 = 3 s and 𝑡 = 4 s ?

What force is applied to the object between 𝑡 = 4 s and 𝑡 = 6 s ?

What average force is applied to the object between 𝑡 = 2 s and 𝑡 = 5 s ? Answer to one decimal place.

What average force is applied to the object between 𝑡 = 2 s and 𝑡 = 7 s ?

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