A body travelling at 54 km/h increases to 108 km/h while travelling a distance of 20 m. the change in momentum is 2250 kg m/s. find the mass and force
Answers
Answer:
- Mass of body = 150 kg
- Force acting = 2531.25 N
Explanation:
Given
- Initial velocity of body, u = 54 km/h = 54 × 5/18 m/s = 15 m/s
- Final velocity of body, v = 108 km/h = 108 × 5/18 m/s = 30 m/s
- Distance covered by body, s = 20 m
- Change in momentum, Δ p = 2250 kg m/s
To find
- Mass of body, m =?
- Force on body, F =?
Formula required
- Third equation of motion
2 a s = v² - u²
- First equation of motion
v = u + a t
- Formula to calculate force
F = Δ p / Δ t = m a
[ Where a is acceleration, s is distance covered, v is final velocity, u is initial velocity, t is time taken or change in time, F is force required, Δ p is change in momentum and m is mass of body ]
Solution
Let, time taken by body for changing velocity be t
and, Let acceleration of body be a
Then, Using third equation of motion
→ 2 a s = v² - u²
→ 2 a (20) = ( 30 )² - ( 15 )²
→ 40 a = 900 - 225
→ 40 a = 675
→ a = 675 / 40
→ a = (135/8) m/s²
Now,
Using first equation of motion
→ v = u + a t
→ 30 = 15 + ( 135/8 ) t
→ t = 15 / (135/8)
→ t = (15 × 8) / 135
→ t = (8/9) sec
Using formula for calculating force
→ F = Δ p / t
→ F = ( 2250 ) / ( 8/9 )
→ F = 2531.25 N
Also, Using formula
→ F = m a
→ 2531.25 = m · (135/8)
→ m = ( 2531.25 × 8 ) / 135
→ m = 150 kg
Therefore,
- Mass of body = 150 kg . and
- Force acting = 2531.25 N.
Answer:
[tex] \huge \fbox {Given} [\tex]
A body travelling at 54 km/h increases to 108 km/h while travelling a distance of 20 m. the change in momentum is 2250 kg m/s. find the mass and force
[tex] \huge \fbox {To find} [L