A blob of mass 5 kg is place on a table top.it is attached to a mass piece of 2kg by a light string that passes over a frictionless pulley.the table top exerts a frictional force of 7 N on the block (a) calculate the accelation of the system
force = 2*9.81 - 7 = 12.6 Newtons
accelerated mass = 5 + 2 = 7
a = F/m = (12.6/7) m/s^2
How do i calculate the tension in the string
To calculate the acceleration of the system, we need to consider the forces acting on each object and apply Newton's second law.
Let's break down the forces acting on each object separately:
1. For the 5 kg block:
- The force of gravity acting on it is given by the equation Fg = m * g, where m is the mass (5 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, Fg = 5 kg * 9.8 m/s^2 = 49 N.
- The frictional force exerted by the table is given as 7 N.
2. For the 2 kg mass:
- The force of gravity acting on it is Fg = m * g, where m is the mass (2 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Hence, Fg = 2 kg * 9.8 m/s^2 = 19.6 N.
Now, let's analyze the system as a whole:
Since the 5 kg block is connected to the 2 kg mass by a light string that passes over a frictionless pulley, the tension in the string is the same for both objects.
Let's denote the tension in the string as T.
For the 5 kg block:
- The net force acting on it is given by the equation Fnet = T - Ff, where Ff is the frictional force (7 N) exerted by the table. Therefore, Fnet = T - 7 N.
Applying Newton's second law, Fnet = ma, where m is the mass (5 kg) and a is the acceleration of the system. Therefore, T - 7 N = 5 kg * a.
For the 2 kg mass:
- The net force acting on it is given by the equation Fnet = Fg - T. Therefore, Fnet = 19.6 N - T.
Applying Newton's second law, Fnet = ma, where m is the mass (2 kg) and a is the acceleration of the system. Therefore, 19.6 N - T = 2 kg * a.
Since the tension is the same for both objects, we can equate the two equations:
T - 7 N = 5 kg * a
19.6 N - T = 2 kg * a
Now, we can solve these two equations simultaneously to find the acceleration (a) of the system.
T - 7 N = 5 kg * a
19.6 N - T = 2 kg * a
Rearranging the equations, we have:
T = 5 kg * a + 7 N
T = 19.6 N - 2 kg * a
Setting them equal to each other:
5 kg * a + 7 N = 19.6 N - 2 kg * a
Combining like terms:
7 kg * a = 12.6 N
Dividing both sides by 7 kg:
a = 12.6 N / 7 kg
Therefore, the acceleration of the system is approximately 1.8 m/s^2.