Question

На вагонетку, масса которой m=400кг, начала действовать постоянная сила F/Под её действием вагонетка прошла путь S=5,5 м и приобрела скорость V=2м/с. НА пути движения коэффициент трения f=0,012. определить работу А этой силы.

Answer 1

Уравнение скорости v=at; a=v/t;
Уравнение движения x=0,5at^2; подставляем ускорение из первого уравнения и получаем x=0,5vt;
t=x/0,5v;
t=5,5/0,5*2;
t=5,5 c;
a=2/5,5 м/с^2;
F=ma;
F=400*2/5,5 Н;
A=FS;
A=5,5*800/5,5 Дж;
A=800; Это работа равнодействующей двух сил: "толкающей" силы и силы трения.
Работа силы трения равна Aт=-0.012mg*S; Aт=-264 Дж.
Значит работа "толкающей" силы равна A=800+264=1064 Дж.

Answer 2

Calculation of Work Done by the Force on the Cart

To determine the work done by the constant force on the cart, we can use the formula:

Work (W) = Force (F) × Distance (S) × cos(θ)

Where: - Force (F) is the constant force acting on the cart. - Distance (S) is the distance traveled by the cart. - θ is the angle between the force vector and the direction of motion of the cart.

In this case, the force acting on the cart is constant, the distance traveled is 5.5 meters, and the force is acting in the same direction as the motion of the cart. Therefore, the angle between the force vector and the direction of motion is 0 degrees.

Using the given values: - Mass of the cart (m) = 400 kg - Distance traveled (S) = 5.5 m - Velocity acquired (V) = 2 m/s - Coefficient of friction (f) = 0.012

We can calculate the work done by the force as follows:

Work (W) = Force (F) × Distance (S) × cos(θ)

Since the angle between the force vector and the direction of motion is 0 degrees, the cosine of 0 degrees is 1. Therefore, we can simplify the equation to:

Work (W) = Force (F) × Distance (S)

To find the force, we can use Newton's second law of motion:

Force (F) = mass (m) × acceleration (a)

The acceleration can be calculated using the equation:

Acceleration (a) = (final velocity (V) - initial velocity (U)) / time (t)

In this case, the initial velocity (U) is 0 m/s, the final velocity (V) is 2 m/s, and the time (t) is not given. Therefore, we cannot directly calculate the acceleration.

However, we can use the equation of motion:

V^2 = U^2 + 2as

Where: - V is the final velocity - U is the initial velocity - a is the acceleration - s is the distance traveled

Rearranging the equation, we get:

a = (V^2 - U^2) / (2s)

Substituting the given values:

a = (2^2 - 0^2) / (2 × 5.5) = 4 / 11 = 0.3636 m/s^2

Now, we can calculate the force:

Force (F) = mass (m) × acceleration (a) = 400 kg × 0.3636 m/s^2 = 145.44 N

Finally, we can calculate the work done by the force:

Work (W) = Force (F) × Distance (S) = 145.44 N × 5.5 m = 799.92 J

Therefore, the work done by the force on the cart is approximately 799.92 Joules.