Solved Questions on Force and Laws of Motion
1. A car of mass 1200 kg accelerates from rest to a velocity of 20 ms-1 in 10 seconds. What is the magnitude of the force applied to the car during this acceleration?
a) 120 N
b) 2400 N
c) 600 N
d) 240 N
Answer: b) To calculate the magnitude of the force applied to the car during its acceleration, we can use Newton's second law of motion, which states that
F = ma
where F is the force applied, m is the mass of the object, and a is the acceleration.
Given:
Mass of the car (m) = 1200 kg
Initial velocity (u) = 0 ms-1
Final velocity (v) = 20 ms-1
Time (t) = 10 s
Acceleration (a) can be calculated using the formula
a = (v−u)/t
Substitute the values:
a = (20 ms-1 − 0 ms-1)/10 s
a = 2 ms-2
Now, use Newton's second law to calculate the force (F):
F = ma
F = 1200 kg × 2 ms-2
F = 2400 N
So, the magnitude of the force applied to the car during its acceleration is 2400 N, and this is the correct answer.
2. A car and a motorcycle are both moving at 60 kmh-1. Which one has greater momentum and why?
a) The car, because it has greater mass.
b) The motorcycle, because it has greater acceleration.
c) Both have the same momentum because they have the same velocity.
d) It depends on the direction of their motion.
Answer: a) Momentum is the product of an object's mass and its velocity. In this case, both the car and the motorcycle are moving at the same velocity of 60 km/h. However, the car has a greater mass compared to the motorcycle. Since momentum depends on both mass and velocity, the car will have greater momentum than the motorcycle.
3. A 20 kg mass is attached to one end of a string that passes over a pulley. The other end of the string is pulled by a force of 300 N. Determine the acceleration of the 20 kg mass. (Take g = 9.8 ms-2)
a) 4.8 ms-2
b) 5.2 ms-2
c) 5 ms-2
d) -5.2 ms-2
Answer: b) To solve this problem, we can follow the steps below:
Calculate the force due to gravity acting on the 20 kg mass:
F (gravity) = m x g = 20 kg x 9.8 ms-2 = 196 N
Calculate the net force applied to the 20 kg mass:
Net Force = F (Applied) - F (gravity) = 300 N - 196 N = 104 N
Apply Newton's second law (F=ma) to find the acceleration (a):
Net Force = m x a
104 N = 20 kg x a
a = 104 N/20 kg
a = 5.2 ms-2
4. After applying a strong upward force, a student launches a ball vertically into the air. What is the accurate statement regarding the ball's condition at the peak of its trajectory?
a) The ball has zero acceleration and zero velocity.
b) The ball has zero acceleration but a non-zero velocity.
c) The ball has a non-zero acceleration and a non-zero velocity.
d) The ball has a non-zero acceleration but zero velocity.
Answer: d) At the highest point of its trajectory, the ball reaches its maximum height and momentarily comes to a stop before reversing direction and descending. At this point, its velocity is zero, but its acceleration due to gravity is still acting on it, even though it's in the opposite direction.
5. Two balls, A and B, collide and bounce off each other. Ball A has a mass of 0.5 kg and was initially moving at 4 ms-1 to the right, while ball B has a mass of 0.8 kg and was initially at rest. After the collision, ball A moves at 1 ms-1. What is the velocity of ball B after the collision?
a) 2.0 ms-2
b) 4.4 ms-1
c) 2.5 ms-2
d) 1.9 ms-1
Answer: d) To solve this problem, we can apply the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision in the absence of external forces.
Initial total momentum = Final total momentum
Let's calculate the initial total momentum of the system:
Initial momentum of ball A = mass of A × initial velocity of A
Initial momentum of A = 0.5 kg × 4 ms-1 = 2 kg ms-1
Initial momentum of ball B = mass of B × initial velocity of B
Initial momentum of B = 0.8 kg × 0 ms-1 = 0 kg ms-1
Initial total momentum = 2 kg ms-1 + 0 kg ms-1 = 2 kg ms-1
Now, let's calculate the final total momentum of the system after the collision:
Final momentum of ball A = mass of A × final velocity of A
Final momentum of A = 0.5 kg × 1 ms-1 = 0.5 kg ms-1
Final momentum of ball B = mass of B × final velocity of B
Let's assume the final velocity of ball B is "v" ms-1.
Final momentum of B = 0.8 kg × v = 0.8v kg ms-1
Final total momentum = 0.5 kg ms-1 + 0.8v kg ms-1 = 0.8v + 0.5 kg ms-1
According to the law of conservation of momentum, initial total momentum = final total momentum:
2 kg ms-1 = 0.8v + 0.5 kg ms-1
Now solve for "v":
2 kg ms-1 - 0.5 kg ms-1 = 0.8v
1.5 kg ms-1 = 0.8v
v = 1.5 kg ms-1 / 0.8
v ≈ 1.875 ms-1
The velocity of ball B after the collision is approximately 1.9 ms-1.
FAQs
1. What are the three laws of motion proposed by Sir Isaac Newton?
Sir Isaac Newton proposed three fundamental principles of motion, which constitute the foundation of classical mechanics:
- Newton's First Law of Motion (Law of Inertia)
- Newton's Second Law of Motion (Law of Acceleration)
- Newton's Third Law of Motion
2. What are the different types of forces?
There are several types of forces, including:
- Contact forces: Such as friction, tension, normal force.
- Non-contact forces: Such as gravity, magnetic force, electrostatic force.
3. What is Newton's First Law of Motion?
Newton's First Law, also known as the Law of Inertia, states that an object will remain at rest or continue moving at a constant velocity unless acted upon by an external force.
4. What is the difference between mass and weight?
Mass refers to the quantity of mass in an item that stays constant regardless of its position. Weight, on the other hand, is the force imposed on an item by gravity, which changes with the gravitational attraction acting on the object.
5. What are some examples of circular motion governed by the laws of motion?
Newton's laws can help us understand circular motion. These principles are used, for example, to describe the motion of a satellite circling the Earth or an automobile turning around a curve.
