EjerciciosFyQ

Force a man must exert to pull a sled (8334)

F_y_Q — 2024-10-23T03:01:15Z

A man pulls a sled up a ramp using a rope attached to the front, as illustrated in the figure.

The sled has a mass of 80 kg. The kinetic friction coefficient between the sled and the ramp is (), the angle between the ramp and the horizontal is , and the angle between the rope and the ramp is . What force must the man exert to keep the sled moving at a constant speed?

To analyze the forces acting on the sled, decompose them according to the system formed by the direction of movement and a perpendicular axis:

The components of the weight and applied force are:

In the direction perpendicular to the ramp, the sum of the forces must be zero. Consider the "y-component" of the weight to solve for the normal force:

In the direction of movement, the sum of the forces must also be zero because the sled moves at a constant speed. This gives:

The friction force is the product of the normal force and the coefficient of friction:

Substitute the known values into the equations to solve for the force exerted by the man:

Acceleration and time taken by a car to increase speed (8329)

F_y_Q — 2024-10-10T03:34:15Z

A car, which has uniformly accelerated motion, increases its speed from 18 km/h to 72 km/h over a straight distance of 37.5 meters. Calculate the time taken for this journey and its acceleration.

To make the problem homogeneous, the first step is to express the speeds in SI units:

You can relate the change in speed and the distance covered with the car's acceleration:

Substitute the values and calculate:

The time needed to make this speed change is:

Substitute and calculate:

Kinetic energy of a moving projectile (8317)

F_y_Q — 2024-09-19T04:20:43Z

Calculate the kinetic energy of an 18 g projectile moving horizontally at .

If you observe the units in the problem statement, you will see that the mass is not expressed in the SI unit of mass. The first thing you need to do is convert it to kg to make the problem homogeneous.

The kinetic energy of the projectile is given by the equation:

You know the necessary data, so you just need to substitute and calculate:

Calculation of braking acceleration (8312)

F_y_Q — 2024-09-16T03:46:33Z

Determine the acceleration of a car, initially moving at a speed of 120 km/h, knowing that it takes 20 seconds to come to a complete stop.

The car will have changed its speed by 120 km/h in those 20 seconds. First, convert the speed to International System units:

The acceleration will be:

Principle of dimensional homogeneity (8304)

F_y_Q — 2024-09-11T10:46:47Z

What is the principle of dimensional homogeneity?

This principle states that equations relating physical quantities must be consistent, meaning that the same dimensions must appear on both sides of the equation. The best way to understand this is through an example.

The speed at which an object moves under the influence of acceleration is:

(Ec. 1)

Speed is the ratio of distance to the time taken to cover it. In terms of dimensions, it is expressed as:

Acceleration is the ratio of the change in speed to the time taken for that change, so it can be expressed as:

If you apply this to equation (Eq. 1), you will have:

As you can see, the dimensions are the same on both sides of the equation.

Efficiency and useful power (8300)

F_y_Q — 2024-09-07T03:10:02Z

A motor is supplied with a power of 1 000 W. If the efficiency of this motor is , calculate the useful power and the lost power.

Efficiency or performance is the ratio between the useful power and the supplied power:

The useful power will be:

The lost power will be the difference between the supplied and the used power:

Calculation of the half-life of a radioactive element (8299)

F_y_Q — 2024-09-04T03:49:25Z

A sample of 300 grams of a radioactive element remains 18.75 grams after 24 hours. Calculate the half-life.

You must use the decay law, but referring to the mass of the substance:

Solving for the value of , you get:

You know that radioactive activity is related to the half-life and this to the half-life period:

Substituting and solving:

Expressed in hours, it will be:

Vertical upward lunch (8289)

F_y_Q — 2024-08-15T05:47:50Z

A body is launched vertically upwards with an initial velocity of . How long will it take to reach its maximum height?

Since it is a vertical upward launch, if you take the initial velocity as positive, the gravitational acceleration must be negative. The velocity of the object at any instant can be obtained from the expression:

The condition for the body to stop ascending is that the velocity is zero; at that moment, it will have reached its maximum height. By imposing this condition on the previous equation, you can solve for the time and calculate it:

Application of Torricelli's theorem (8284)

F_y_Q — 2024-08-12T02:53:41Z

A cylindrical container is filled with a liquid up to a height of one meter from the base of the container. Then, a hole is made at a point 80 cm below the liquid level:

a) What is the exit velocity of the liquid through the hole?

b) At what distance from the container will the first drop of liquid that touches the ground fall?

a) The exit velocity of the liquid through the hole is given by the expression:

Since the hole is made at a distance of 0.8 m from the liquid level:

b) To calculate the distance at which the first drop falls, you must consider that it follows a motion similar to a horizontal launch. In this case, the position with respect to the X and Y axes follows the equations:

Since you know that the drop starts at a height of 0.2 m:

To find the horizontal position, substitute this time:

Relationship between linear and angular quantities (7425)

F_y_Q — 2021-12-10T07:07:49Z

A car starts at and uniformly accelerates at for 5 s.

a) Calculate the final velocity and the displacement of the car.

b) Determine the diameter of the tire if the angular displacement is 60 radians.

c) Calculate the final angular velocity and angular acceleration of the tires.

a) The equation for calculating the final velocity is:

Just replace the data and calculate:

The equation for calculating the displacement is:

Using the data in the problem statement:

b) You must relate the distance covered to the radius of the wheel:

Diameter is two times the radius:

c) The final angular velocity is:

The angular acceleration is:

Descarga el enunciado y la resolución del problema en formato EDICO si lo necesitas.