A heavy wooden block rests on a flat table and a high-speed bullet is fired horizontally into the block, the bullet stopping in it. How far will the block slide before coming to a stop? The mass of the bullet is 9.5 g, the mass of the block is 10.5 kg, the bullet's impact speed is 610 m/s, and the coefficient of kinetic friction between the block and the table is 0.220
a 50kg boy suspends himself from a rope tied horizontally between two vertical poles. The two segments of the rope are then inclined at angles 30 degrees and 60 degree respectively to the horizontal.the tensions fas in the segments of the rope
To calculate how far the block will slide before coming to a stop, we need to consider the conservation of momentum and the friction acting on the block.
First, let's calculate the initial momentum of the bullet before it hits the block. The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v.
The mass of the bullet is given as 9.5 g, which is equivalent to 0.0095 kg. The bullet's impact speed is 610 m/s.
So, the initial momentum of the bullet is: p_bullet = 0.0095 kg * 610 m/s.
Since the bullet stops after hitting the block, its final momentum is zero.
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, the initial momentum of the bullet is equal to the momentum of the combined system (bullet + block) after the collision.
Now, we can calculate the velocity of the block after the collision. The mass of the block is given as 10.5 kg.
Since the bullet stops in the block, the mass of the whole system after the collision is the sum of the bullet's mass and the block's mass.
So, the final velocity (v_f) of the block can be calculated using the equation: p_bullet = (m_bullet + m_block) * v_f.
Since we know the initial momentum of the bullet and the masses of the bullet and block, we can solve for v_f.
Next, we need to calculate the force of friction acting on the block.
The force of friction (F_friction) can be calculated using the equation: F_friction = coefficient of kinetic friction * normal force.
The normal force is the force exerted by the table on the block, which is equal to the weight of the block (mass_block * acceleration due to gravity).
The coefficient of kinetic friction is given as 0.220.
Once we calculate the force of friction, we can determine the acceleration (a) of the block using Newton's second law of motion: F_net = mass_block * a.
Since the force of friction is the only force acting on the block (in the horizontal direction), it will be the net force.
Finally, we can calculate the distance (d) the block will slide using the kinematic equation: d = (v_f^2 - v_0^2) / (2 * a), where v_0 is the initial velocity of the block (which is zero, as it is at rest initially).
By plugging in the values for v_f, a, and v_0, we can find the distance the block will slide before coming to a stop.