When a constant force acts on an object, what does the object’s
change in momentum depend upon? check all that
apply check all that
apply check all that
apply The change in momentum depends upon the magnitude of the force.
The change in momentum depends upon the change in the position of
the object.
The change in momentum depends upon the time interval during which
the force acts.
The change in momentum depends upon the change in the velocity of
the object.
The change in momentum depends upon the mass of the object.
General guidance
Concepts and reason
The concepts used to solve this problem are Newton’s second law and change in momentum.
Initially, use the relation between force and change in momentum, then use the Newton’s second law, finally compare the change in momentum and Newton’s law to determine and check whether the given statement is right or wrong.
Fundamentals
The Newton’s second law states that the rate of change of momentum of a body is directly proportional to the force applied. This can be expressed as given below:
Here, is the force, which acts on an object and is the rate of change of momentum.
The expression for the momentum is given below:
Here, is the momentum of the object, is the mass of the object and is the velocity of the object.
According to the Newton’s second law, the relation between force and acceleration is expressed as follows:
Here, is the acceleration of the object.
Step-by-step
Step 1 of 4
The rate of change of momentum of a body is directly proportional to the force applied. This can be expressed as follows:
…… (1)
The expression for the momentum is given below:
Replace for in Equation (1) and rewrite it.
Here, is the rate of change of velocity.
Use for in the above equation.
…… (2)
Compare Equations (1) and (2).
From the above equation, the incorrect statement is given below:
• The change in momentum depends upon the change in the position of the object.
Hence, the correct statement is given below:
• The change in momentum depends upon the magnitude of the force.
The change in momentum depends upon the magnitude of the force.
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force and inversely proportional to the mass of the object.
The incorrect expression for the momentum is . The correct expression is .
Use the expression to determine the correct statement from the given options.
Step 2 of 4
The relation between change in momentum and force is given below:
From the above equation, the correct statement is given below:
• The change in momentum depends upon the time interval during which the force acts.
The change in momentum depends upon the time interval during which the force acts.
The constant force acts on the object is directly proportional to the change in momentum.
Do not consider the relation between force and impulse because it is incorrect. The correct relation is between force and change in momentum.
Use the relation between change and momentum and velocity, and determine the correct statement from the given options.
Step 3 of 4
The expression for the momentum is given below:
From the above equation, the correct statement is given below:
• The change in momentum depends upon the change in the velocity of the object.
The change in momentum depends upon the change in the velocity of the object.
The momentum is directly proportional to the velocity and mass of the given particle.
The size of the change in momentum depends on the size of the resultant force and the time for which the force acts.
The incorrect expression for the momentum is . Hence, the correct expression is .
Use the expression to determine the correct statement from the given options.
Step 4 of 4
The expression for the momentum is given below:
From the above equation, the correct statement is given below:
• The change in momentum depends upon the mass of the object.
The change in momentum depends upon the mass of the object.
The momentum is directly proportional to the mass of the given particle.
Momentum of the object is equal to the mass of the object times the velocity of the object.
Do not consider the momentum depends on the variable of mass and acceleration; Hence, the correct statement is that the momentum depends on the variable of mass and velocity.
Answer
The change in momentum depends upon the magnitude of the force.
The change in momentum depends upon the time interval during which the force acts.
The change in momentum depends upon the change in the velocity of the object.
The change in momentum depends upon the mass of the object.
Answer only
The change in momentum depends upon the magnitude of the force.
The change in momentum depends upon the time interval during which the force acts.
The change in momentum depends upon the change in the velocity of the object.
The change in momentum depends upon the mass of the object.
dp dt
F
dp/dt
р-ту
р
т
V
F =ma та
F dp/dt
р-ту
dp dt
р-ту
ту
р
d(mv) F = dt dv — т
dv/dt
dv/dt
F =ma та
ma – Фр dt dp %3D тadt dp Fdt
p m/v
р-ту
dp = Fdt
dp = Fdt
Ар %3D тАу
Aр – т(у/)
Ар %3D тАу
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