3 questions about The resultant force equation
1. A car with a mass of 5 tonnes moves from rest in 50 seconds, reaching a speed of 72 km/hour. The force on the car is…
Known:
Mass (m) = 5 tons = 5000 kg
Initial speed (vo) = 0
Final speed (vt) = 72 km/h = 20 m/s
Time interval (t) = 50 seconds
Wanted: Force (F)
Solution:
Calculate the acceleration using the Non Uniform Linear Motion formula:
vt = vo + a t
20 = 0 + a (50)
20 = 50 a
a = 20 / 50 = 0,4 m/s2
Calculate the resultant force using Newton’s second law formula:
ΣF = m a
F = (5000)(0,4) = 2000 Newton
2. A car has a mass of 1 ton, for 4 seconds its speed increases uniformly from 10 m/s to 18 m/s. Determine the magnitude of the force that accelerates the car.
Known:
The mass of the car (m) = 1 ton = 1000 kg
Time interval (t) = 4 seconds
Initial velocity (vo) = 10 m/s
Final velocity (vt) = 18 m/s
Wanted: Force (F)
Solution:
Calculate the acceleration using the Non Uniform Linear Motion formula:
vt = vo + a t
18 = 10 + a (4)
18 – 10 = a (4)
8 = 4 a
a = 8 / 4 = 2 m/s2
Calculate the resultant force using Newton’s second law formula:
ΣF = m a
F = (1000)(2) = 2000 Newton
3. The two force vectors are perpendicular to each other which results in a resultant of 10 N. If one of the force vectors is 6 N , determine the magnitude of the other force vector.
Known:
Resultant force (F) = 10 N
Force 1 (F1) = 6 N
Wanted: Force 2 (F2)
Solution:
F2 = 10 – 6 = 4 Newton
