you have to push a cart, that is at rest, to a speed of 15 ms^-1 to win a bet with your friend. But you only have 30 seconds to do it. if the mass of the cart is 20kg what is the minimum amount of force you need to apply on the cart to win the bet?
Answers
Required Answer :
• Minimum amount of force you need to apply on the cart to win the bet = 10 N
Given :
• Initial velocity of the cart = 0 m/s [The car was initially at rest, so the initial velocity will be zero.]
• Final velocity of the cart = 15 m/s
• Time = 30 seconds
• Mass of the cart = 20 kg
To find :
• Minimum amount of force you need to apply on the cart to win the bet
Solution :
Here, we have to find the minimum amount of force required to apply on the cart to win the bet. So, firstly we will calculate the acceleration of the cart by using the first equation of motion.
First equation of motion :-
- v = u + at
where,
- v denotes the final velocity
- u denotes the initial velocity
- a denotes the acceleration
- t denotes the time taken
we have,
- v = 15 m/s
- u = 0 m/s
- t = 30 s
Substituting the given values :-
→ 15 = (0) + (a)(30)
→ 15 = 30 × a
→ 15/30 = a
→ 1/2 = a
→ 0.5 = a
The acceleration of the cart = 0.5 m/s²
Now, using the formula :-
- F = ma
where,
- F denotes the force
- m denotes the mass
- a denotes the acceleration
we have,
- m = 20 kg
- a = 0.5 m/s²
Substituting the given values :-
→ Force = 20 × 0.5
→ Force = 10
The force you need to apply on the cart to win the bet = 10 N