You are the lead scientist for a criminal investigation unit. Your team has found what might be the gun that caused the murder.Unfortunately the bullet that identifies the gun can not be found,but there is enough evidence that if you can figure out the speed of the bullet at a distance of 100 meters from where the gun was fired,you will solve the case.
If you could figure out the exact point the gun was aimed, then you could measure the drop in 100yards.
A block weighing 130 Newtons on an incline is held back by a weight of 45 newton hanging from a cord tha passes over a frctionless pulley nd is attached to the blcok. Find the angle at which the block will slide down the plane at constant speed. the answer is 49 degrees, but I don't know how the textbook got there.
To solve this problem, you can use the concept of equilibrium. The block will slide down the incline plane at a constant speed when the forces acting on it are balanced.
First, break down the forces acting on the block. We have the gravitational force (weight) acting vertically downward, which is 130 N in this case. Additionally, we have the tension force in the cord, which is pulling the block up the incline.
Let's consider the forces along the incline plane. The weight of the block can be resolved into two components: one acting parallel to the plane and the other perpendicular to the plane. The component acting perpendicular to the plane does not affect the motion, as it is balanced by the normal force from the incline.
The component of weight acting parallel to the plane is given by:
Weight_parallel = Weight * sin(angle),
where angle is the angle of the incline plane.
Next, the tension force in the cord can be considered as acting parallel to the plane, opposing the component of the weight:
Tension_force = Weight_parallel.
Since we want the block to slide down the plane at a constant speed, the net force on the block in the horizontal direction should be zero.
The net force acting in the horizontal direction can be calculated as the difference between the force parallel to the plane (Weight_parallel) and the force of friction:
Net_force = Weight_parallel - Friction_force.
At constant speed, the friction force is given by:
Friction_force = coefficient_of_friction * Normal_force.
Since the block is moving at a constant speed, we know that the friction force is equal to the tension force:
Friction_force = Tension_force.
Therefore:
Weight_parallel - Tension_force = Tension_force.
Now, with the given weight of the block (130 N), we can calculate the weight parallel to the plane for different angles and compare it to the tension force.
For the given answer of 49 degrees, let's calculate the weight parallel to the plane:
Weight_parallel = Weight * sin(angle)
= 130 N * sin(49 degrees)
≈ 93.97 N.
Comparing this to the tension force, we can see that they are equal, which means the forces are balanced in the horizontal direction. This indicates that the block will slide down the plane at a constant speed.
If you have any further questions or need clarification, please let me know.