A steel

A steel hammer with a weight of 0.5 kg hits the nail at a speed of 3 m/s. How deep the nail penetrates the wood if the hammer acts on the nail with an average force of 50N.

Correct result:

x =  45 mm

Solution:

$$\begin{gathered} m=0.5\text{ kg } \\ v=3\text{ m/s } \\ F=50\text{ N } \\ {E}_1=1\mathrm{/}2\cdot m\cdot v^2=1\mathrm{/}2\cdot 0.5\cdot 3^2={\displaystyle \frac{9}{4}}=2.25\text{ J } \\ {E}_1=F_x \\ {x}_1=E_1\mathrm{/}F=2.25\mathrm{/}50={\displaystyle \frac{9}{200}}=0.045\text{ m } \\ x=1000\cdot x_1=1000\cdot 0.045=45\text{ mm} \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Here is
  Here is a data set (n=117) that has been sorted. 10.4 12.2 14.3 15.3 17.1 17.8 18 18.6 19.1 19.9 19.9 20.3 20.6 20.7 20.7 21.2 21.3 22 22.1 22.3 22.8 23 23 23.1 23.5 24.1 24.1 24.4 24.5 24.8 24.9 25.4 25.4 25.5 25.7 25.9 26 26.1 26.2 26.7 26.8 27.5 27.6 2
• Shot
  Shot with a mass 43 g flying at 256 m/s penetrates into the wood to a depth 25 cm. What is the average force of resistance of wood?
• Elevator
  In homes with more floor elevators are used. For passenger transport, the most commonly used traction elevator counterweight. The top of the shaft engine room with the engine. The car is suspended on a rope, which is guided up over two pulleys to the coun
• Accelerated motion - mechanics
  The delivery truck with a total weight of 3.6 t accelerates from 76km/h to 130km/h in the 0.286 km long way. How much was the force needed to achieve this acceleration?
• Car
  At what horizontal distance reaches the car weight m = 753 kg speed v = 74 km/h when the car engine develops a tensile force F = 3061 N. (Neglect resistance of the environment.)
• Angled cyclist turn
  The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?
• Center of gravity
  The mass points are distributed in space as follows - specify by coordinates and weight. Find the center of gravity of the mass points system: A₁ [1; -20; 3] m₁ = 46 kg A₂ [-20; 2; 9] m₂ = 81 kg A₃ [9
• Friction coefficient
  What is the weight of a car when it moves on a horizontal road at a speed of v = 50 km/h at engine power P = 7 kW? The friction coefficient is 0.07
• Speed of Slovakian trains
  Rudolf decided to take the train from the station 'Ostratice' to 'Horné Ozorovce'. In the train timetables found train Os 5409 : km 0 Chynorany 15:17 5 Ostratice 15:23 15:23 8 Rybany 15:27 15:27 10 Dolné Naštice 15:31 15:31 14 Bánovce nad Bebravou 15:35 1
• Two runners
  Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 min
• Inclined plane
  1. How much work W we have to do to pull a body weighing 200 kg along an inclined plane with a length of 4 m to a total height of 1.5 m. 2. Find the force we need to exert to do this if we neglect frictional resistance. 3. Find the force we would need if
• Znojmo
  From Znojmo to Brno started truck with a trailer at an average speed 53 km per hour. Against him 14 minutes later from Brno started car with an average speed of 1.2-times greater than the truck. How long and how far from Znojmo, they meet if the distance
• The bridge
  A vehicle weighing 5,800 kg passes 41 km/h on an arched bridge with a radius of curvature of 62 m. What force is pushing the car onto the bridge as it passes through the center? What is the maximum speed it can cross over the center of the bridge so that
• Overload
  What overload in g (g-force) has passed the pilot if he accelerated from 0 to 600 km/h in 3 seconds?
• Centroid - two bodies
  A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravi
• The swimmer
  The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, the river width is 90 m. a) What is the resulting speed of the swimmer with respect to the tree on the riverbank when the swimmer motion
• Concrete column
  The concrete column of the highway bridge has the shape of a block with dimensions of 1m x 0.8m x 25m. It should be lifted by crane to a height of 20m. What is the power of his engine if the lifting takes 2 minutes?