A dray horse is being pulled by a rope across a level plow field by a force of 750.0N exerted at an angle of 47° above the horizontal. If the horse’s velocity is constant and the coefficient of friction is ì=.21, determine the mass of the horse.
Wt. = m*g = m*9.8 = Wt. in Newtons.
Fp = 9.8m*sin(0) = 0 = Force parallel to the field.
Fv=9.8m*cos(0) - 750*sin47 = 9.8m-548.5=
Force perpendicular to the field.
Fk = u*Fv=0.21(9.8m-548.5)=2.06m-115.19 = Force of kinetic energy.
750*cos47-Fp-Fk = m*a
511.5-0-(2.06m-115.19) = m*0
511.5 - 2.06m+115.19 = 0
2.06m = 626.7
m = 304 kg.
To determine the mass of the horse, we can start by analyzing the forces acting on the horse.
1. First, let's consider the gravitational force acting on the horse. According to Newton's second law of motion, the gravitational force can be calculated using the equation F_gravity = m * g, where m is the mass of the horse and g is the acceleration due to gravity (approximately 9.8 m/s²).
2. The frictional force opposing the motion of the horse can be calculated using the equation F_friction = ì * F_normal, where ì is the coefficient of friction and F_normal is the normal force. In this case, since the horse is on a level field, the normal force is equal to the gravitational force, so F_normal = F_gravity.
3. The applied force, which is exerted by the rope at an angle of 47° above the horizontal, can be divided into its horizontal and vertical components. The horizontal component of the applied force (F_horizontal) will help overcome the frictional force.
4. Since the horse is moving with a constant velocity, the net force acting on it must be zero. This means that the horizontal component of the applied force must equal the frictional force: F_horizontal = F_friction.
Now, let's calculate the mass of the horse using the given information:
Given:
Force applied (F_applied) = 750.0 N
Angle (θ) = 47°
Coefficient of friction (ì) = 0.21
Step 1: Calculate the horizontal and vertical components of the applied force.
F_horizontal = F_applied * cos(θ)
F_vertical = F_applied * sin(θ)
Step 2: Calculate the frictional force.
F_friction = ì * F_gravity, where F_gravity = m * g
Step 3: Set the horizontal component of the applied force equal to the frictional force, since they have the same magnitude.
F_horizontal = F_friction
Step 4: Substitute the calculated values into the equation and solve for mass.
F_applied * cos(θ) = ì * (m * g)
Now, let's solve the equation:
750.0 N * cos(47°) = 0.21 * (m * 9.8 m/s²)
m = (750.0 N * cos(47°)) / (0.21 * 9.8 m/s²)
After performing the calculations, the mass of the horse will be determined.