A 8.30 kg object with a speed of 34.0 m/s strikes a steel plate at an angle of 45.0 degrees with the normal to the plate, and rebounds at the same speed and angle on the other side of the normal. What is the change (in magnitude only) of the linear momentum of the object (in kilogram-meters/second)?
To determine the change in magnitude of the linear momentum of the object, we first need to calculate the initial and final linear momentum values separately. Then, we can find the difference between the two values.
The formula to calculate linear momentum is given by:
Linear momentum (p) = mass (m) × velocity (v)
Given:
Mass of the object (m) = 8.30 kg
Initial speed (v) = 34.0 m/s
1. Calculate the initial linear momentum:
Initial linear momentum (p_initial) = mass × initial velocity
p_initial = 8.30 kg × 34.0 m/s
2. Determine the final speed:
The object rebounds with the same speed, so the final speed remains 34.0 m/s.
3. Calculate the final linear momentum:
Final linear momentum (p_final) = mass × final velocity
p_final = 8.30 kg × 34.0 m/s
4. Find the change in magnitude of linear momentum:
Change in magnitude of linear momentum (Δp) = |p_final| - |p_initial|
Note that we take the absolute value to ensure we are finding the magnitude (positive value) of the change, as the question requests.
Therefore,
Δp = |p_final| - |p_initial|
Plug in the values to calculate Δp.