The velocity of a 629-kg auto is changed from 10.0 m/s to 44.0 m/s in 70.0 s by an external, constant force.
(a) What is the resulting change in momentum of the car?
(b) What is the magnitude of the force?
To find the resulting change in momentum of the car, you can use the equation for momentum:
Momentum (p) = mass (m) * velocity (v)
(a) So the change in momentum (Δp) is given by:
Δp = m * Δv
Where m is the mass of the car and Δv is the change in velocity.
Given:
Mass of the car (m) = 629 kg
Initial velocity (v1) = 10.0 m/s
Final velocity (v2) = 44.0 m/s
First, calculate the change in velocity (Δv):
Δv = v2 - v1
Δv = 44.0 m/s - 10.0 m/s
Δv = 34.0 m/s
Substituting the values into the formula for Δp:
Δp = m * Δv
Δp = 629 kg * 34.0 m/s
Therefore, the resulting change in momentum of the car is:
Δp = 21386 kg·m/s
(b) To find the magnitude of the force (F) applied to the car, you can use the equation relating force, mass, and acceleration:
Force (F) = mass (m) * acceleration (a)
Since acceleration (a) is the change in velocity (Δv) divided by the time (t):
a = Δv / t = 34.0 m/s / 70.0 s
Substituting the values for the acceleration:
F = m * a
F = 629 kg * (34.0 m/s / 70.0 s)
Therefore, the magnitude of the force applied to the car is:
F ≈ 305.14 N (rounded to two decimal places)
To find the change in momentum of the car (Δp), we can use the equation:
Δp = m * Δv
Where:
m = mass of the car = 629 kg
Δv = change in velocity = final velocity - initial velocity = 44 m/s - 10 m/s = 34 m/s
(a) Calculating Δp:
Δp = 629 kg * 34 m/s = 21,386 kg·m/s
The resulting change in momentum of the car is 21,386 kg·m/s.
To find the magnitude of the force (F), we can use the equation:
F = Δp / Δt
Where:
Δp = change in momentum = 21,386 kg·m/s
Δt = time interval = 70 s
(b) Calculating F:
F = 21,386 kg·m/s / 70 s ≈ 305.5 N
The magnitude of the force acting on the car is approximately 305.5 N.