a 10-kg block on a perfectly smooth horizontal table is connected by a horizontal string to a 63-kg block that is hanging over the edge of the table. What is the magnitude of the acceleration of the 10-kg block when the other block is gently released?
8.5 m/sec^2
by drawing both free body diagram, and using newtons second law Fnet = ma,
box 1
Ft = m1a
box 2
Ft - m2g = -m2a (because its moving down )
Ft = m2g - m2a
combining both boxes by replacing ft of box 2 in box 1 equation:
m2g - m2a = m1a
m2g = a(m1 + m2)
a = m2g / m1 + m2, use this equation and replace the number to get the acceleration value.
hope this was helpful !
force down = m g = 63*9.81 N
mass accelerated = 63+10 = 73 kg
a = F/m = 9.81 (63/73) m/s^2
Well, let me break it down for you. When the 63-kg block is released, gravity will try to pull it downwards. As a result, the tension in the string will give it a little push.
Now, because the table is perfectly smooth, there won't be any friction acting on the 10-kg block. So, the only force acting on it is the tension from the string.
Newton's second law tells us that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In this case, the net force acting on the 10-kg block is the tension from the string.
So, the magnitude of the acceleration of the 10-kg block will depend on how much force the tension from the string provides. To find that, we need to calculate the force acting on the 63-kg block due to gravity.
Using the formula F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity, we find that the force acting on the 63-kg block is approximately (63 kg) * (9.8 m/s²) = 617.4 N.
Since the string is connected to both blocks, the force provided by the tension will be the same for both blocks. Therefore, the magnitude of the acceleration of the 10-kg block will also be 617.4 N, assuming the string doesn't break.
But remember, this is a theoretical calculation. In reality, it might take a moment for the tension in the string to fully act on the 10-kg block, so the initial acceleration might not be exactly 617.4 N. Just something to keep in mind, even though the numbers might seem quite weighty!
To determine the magnitude of the acceleration of the 10-kg block when the other block is released, we can start by analyzing the free-body diagram of each block.
Let's denote the 10-kg block as Block A and the 63-kg block as Block B.
Block A:
- Forces acting on Block A are the tension force in the string (T) and the weight force (W_A = m_A * g, where m_A is the mass of Block A and g is the acceleration due to gravity).
Block B:
- Forces acting on Block B are the tension force in the string (T) and the weight force (W_B = m_B * g, where m_B is the mass of Block B).
Since the two blocks are connected, they experience the same tension force (T) in the string.
When Block B is released and starts to move downward, the tension force will cause Block A to accelerate to the right.
To find the tension force (T), we need to consider the forces acting on Block B only. Since Block B is in vertical motion, the net force on it must be equal to its mass multiplied by its acceleration (Newton's second law, F_net = m_B * a):
T - W_B = m_B * a
Substituting W_B = m_B * g:
T - m_B * g = m_B * a ----------(1)
Since Block A and Block B are connected, the tension force (T) also causes Block A to accelerate. Since Block A has a mass of 10 kg, the net force on Block A can be written as:
T = m_A * a_A ----------(2)
Substituting the value of T from equation (2) into equation (1):
m_A * a_A - m_B * g = m_B * a
Since both blocks have the same acceleration (a_A = a), we can simplify the equation:
a * (m_A - m_B) = m_B * g
Finally, we solve for the magnitude of the acceleration (a):
a = (m_B * g) / (m_A - m_B)
Substituting the given values, where m_A = 10 kg and m_B = 63 kg, and using the standard gravity value of g = 9.8 m/s^2, we can calculate the magnitude of the acceleration:
a = (63 kg * 9.8 m/s^2) / (10 kg - 63 kg) = (617.4 N) / (-53 kg) ≈ -11.64 m/s^2
Therefore, the magnitude of the acceleration of the 10-kg block is approximately 11.64 m/s^2 to the left.