Question

An upward force of 32.6 N is applied via a string to lift a ball with a mass of 2.8 kg. (a) What is the gravitational force acting on the ball? (b) What is the net force acting upon the ball? (c) What is the acceleration of the ball?

Answer 1

Answer:

a) Fg = -27.4 N

b) Fnet = 5.2 N

c) a = 1.9 m/s2

Explanation:

a)

• There are two forces acting on the ball, one directed upward (assuming this direction as positive, along the y-axis) which is the tension on the string (lifting force), and another aimed downward, which is the attractive force due to gravity.
• Applying the Newton's Universal Law of Gravitation to a mass close to the surface of the Earth (in this case the ball), we can take the acceleration due to gravity like a constant, that we call by convention g, equal to -9.8 m/s2.
• So, we can write the following expression for Fg:

       $F_{g} = m*g = 2.8 kg*(-9.8m/s2) = -27.4 N (1)$

b)

• The net force on the ball, will be just the difference between the lifting force (32.6 N) and the force due to gravity, Fg:

       $F_{net} = T -F_{g} = 32.6 N - 27.4 N = 5.2 N (2)$

c)

• According Newton's 2nd Law, the acceleration caused by a net force on a point mass (we can take the ball as one) is given by the following expression:

       $a = \frac{F_{net} }{m} = \frac{5.2N}{2.8kg} = 1.9 m/s2 (3)$